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Commuting probability for subrings and quotient rings

Yıl 2017, Cilt: 4 Sayı: 2 (Special Issue: Noncommutative rings and their applications), 189 - 196, 10.01.2017
https://doi.org/10.13069/jacodesmath.284962

Öz

We prove that the commuting probability of a finite ring is no larger than
the commuting probabilities of its subrings and quotients, and characterize
when equality occurs in such a comparison.

Kaynakça

  • [1] S. M. Buckley, Distributive algebras, isoclinism, and invariant probabilities, Contemp. Math. 634 (2015) 31–52.
  • [2] S. M. Buckley, D. MacHale, Commuting probabilities of groups and rings, preprint.
  • [3] S. M. Buckley, D. MacHale, Á. Ní Shé, Finite rings with many commuting pairs of elements, preprint.
  • [4] J. D. Dixon, Probabilistic group theory, C. R. Math. Acad. Sci. Soc. R. Can. 24(1) (2002) 1–15.
  • [5] P. Erdös, P. Turán, On some problems of a statistical group–theory, IV, Acta Math. Acad. Sci. Hung. 19(3) (1968) 413–435.
  • [6] R. M. Guralnick, G. R. Robinson, On the commuting probability in finite groups, J. Algebra 300(2) (2006) 509–528.
  • [7] K. S. Joseph, Commutativity in non–abelian groups, PhD thesis, University of California, Los Angeles, 1969.
  • [8] D. MacHale, How commutative can a non–commutative group be? Math. Gaz. 58(405) (1974) 199–202.
  • [9] D. MacHale, Commutativity in finite rings, Amer. Math. Monthly 83(1) (1976) 30–32.
  • [10] D. Rusin, What is the probability that two elements of a finite group commute?, Pacific J. Math. 82(1) (1979) 237–247.
Yıl 2017, Cilt: 4 Sayı: 2 (Special Issue: Noncommutative rings and their applications), 189 - 196, 10.01.2017
https://doi.org/10.13069/jacodesmath.284962

Öz

Kaynakça

  • [1] S. M. Buckley, Distributive algebras, isoclinism, and invariant probabilities, Contemp. Math. 634 (2015) 31–52.
  • [2] S. M. Buckley, D. MacHale, Commuting probabilities of groups and rings, preprint.
  • [3] S. M. Buckley, D. MacHale, Á. Ní Shé, Finite rings with many commuting pairs of elements, preprint.
  • [4] J. D. Dixon, Probabilistic group theory, C. R. Math. Acad. Sci. Soc. R. Can. 24(1) (2002) 1–15.
  • [5] P. Erdös, P. Turán, On some problems of a statistical group–theory, IV, Acta Math. Acad. Sci. Hung. 19(3) (1968) 413–435.
  • [6] R. M. Guralnick, G. R. Robinson, On the commuting probability in finite groups, J. Algebra 300(2) (2006) 509–528.
  • [7] K. S. Joseph, Commutativity in non–abelian groups, PhD thesis, University of California, Los Angeles, 1969.
  • [8] D. MacHale, How commutative can a non–commutative group be? Math. Gaz. 58(405) (1974) 199–202.
  • [9] D. MacHale, Commutativity in finite rings, Amer. Math. Monthly 83(1) (1976) 30–32.
  • [10] D. Rusin, What is the probability that two elements of a finite group commute?, Pacific J. Math. 82(1) (1979) 237–247.
Toplam 10 adet kaynakça vardır.

Ayrıntılar

Konular Mühendislik
Bölüm Makaleler
Yazarlar

Stephen M. Buckley

Desmond Machale

Yayımlanma Tarihi 10 Ocak 2017
Yayımlandığı Sayı Yıl 2017 Cilt: 4 Sayı: 2 (Special Issue: Noncommutative rings and their applications)

Kaynak Göster

APA Buckley, S. M., & Machale, D. (2017). Commuting probability for subrings and quotient rings. Journal of Algebra Combinatorics Discrete Structures and Applications, 4(2 (Special Issue: Noncommutative rings and their applications), 189-196. https://doi.org/10.13069/jacodesmath.284962
AMA Buckley SM, Machale D. Commuting probability for subrings and quotient rings. Journal of Algebra Combinatorics Discrete Structures and Applications. Mayıs 2017;4(2 (Special Issue: Noncommutative rings and their applications):189-196. doi:10.13069/jacodesmath.284962
Chicago Buckley, Stephen M., ve Desmond Machale. “Commuting Probability for Subrings and Quotient Rings”. Journal of Algebra Combinatorics Discrete Structures and Applications 4, sy. 2 (Special Issue: Noncommutative rings and their applications) (Mayıs 2017): 189-96. https://doi.org/10.13069/jacodesmath.284962.
EndNote Buckley SM, Machale D (01 Mayıs 2017) Commuting probability for subrings and quotient rings. Journal of Algebra Combinatorics Discrete Structures and Applications 4 2 (Special Issue: Noncommutative rings and their applications) 189–196.
IEEE S. M. Buckley ve D. Machale, “Commuting probability for subrings and quotient rings”, Journal of Algebra Combinatorics Discrete Structures and Applications, c. 4, sy. 2 (Special Issue: Noncommutative rings and their applications), ss. 189–196, 2017, doi: 10.13069/jacodesmath.284962.
ISNAD Buckley, Stephen M. - Machale, Desmond. “Commuting Probability for Subrings and Quotient Rings”. Journal of Algebra Combinatorics Discrete Structures and Applications 4/2 (Special Issue: Noncommutative rings and their applications) (Mayıs 2017), 189-196. https://doi.org/10.13069/jacodesmath.284962.
JAMA Buckley SM, Machale D. Commuting probability for subrings and quotient rings. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017;4:189–196.
MLA Buckley, Stephen M. ve Desmond Machale. “Commuting Probability for Subrings and Quotient Rings”. Journal of Algebra Combinatorics Discrete Structures and Applications, c. 4, sy. 2 (Special Issue: Noncommutative rings and their applications), 2017, ss. 189-96, doi:10.13069/jacodesmath.284962.
Vancouver Buckley SM, Machale D. Commuting probability for subrings and quotient rings. Journal of Algebra Combinatorics Discrete Structures and Applications. 2017;4(2 (Special Issue: Noncommutative rings and their applications):189-96.

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